On the topology of components of some Springer fibers and their relation to Kazhdan–Lusztig theory

Abstract

We describe the irreducible components of Springer fibers for hook and two-row nilpotent elements of gl n( C) as iterated bundles of flag manifolds and Grassmannians. We then relate the topology (in particular, the intersection homology Poincaré polynomials) of the pairwise intersections of these components with the inner products of the Kazhdan–Lusztig basis elements of irreducible representations of the rational Iwahori–Hecke algebra of type A corresponding to the hook and two-row Young shapes.